Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:

import java.io.*;    //PrintWriter
import java.math.*;  //BigInteger, BigDecimal
import java.util.*;  //StringTokenizer, ArrayList


public class R230_Div2_B //Name: Three matrices
{	
	FastReader in;
	PrintWriter out;
	
	public static void main(String[] args)  {
		new R230_Div2_B().run();
	}
	
	void run()
	{		
		in = new FastReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}
	
	void solve()
	{
		int n = in.nextInt();	

		int[][] w = new int[n][n];
		double[][] a = new double[n][n];
		double[][] b = new double[n][n];
		
		for (int i = 0; i < n; i++) 
			for (int j = 0; j < n; j++)
				w[i][j] = in.nextInt();
		
		for (int i = 0; i < n; i++) 
			for (int j = i; j < n; j++)
				if (i == j) 
					a[i][j] = w[i][j];
				else
				{
					double mid = (w[i][j] + w[j][i]) / 2.0;
					a[i][j] = mid;
					a[j][i] = mid;
					b[i][j] = w[i][j] - a[i][j];
					b[j][i] = w[j][i] - a[j][i];
				}
			
		
		for (int i = 0; i < n; i++) 
		{
			for (int j = 0; j < n; j++)
				out.print(a[i][j]+ " ");
			out.println();
		}
		for (int i = 0; i < n; i++) 
		{
			for (int j = 0; j < n; j++)
				out.print(b[i][j]+ " ");
			out.println();
		}	
	}

	//-----------------------------------------------------
	void runWithFiles() {
		in = new FastReader(new File("input.txt"));
		try {
			out = new PrintWriter(new File("output.txt"));
		} 
		catch (FileNotFoundException e) {
			e.printStackTrace();
		}
		solve();
		out.close();
	}
	
	class FastReader
	{
	    BufferedReader br;
	    StringTokenizer tokenizer;
	    
	    public FastReader(InputStream stream)
	    {
	        br = new BufferedReader(new InputStreamReader(stream));
	        tokenizer = null;
	    }
		public FastReader(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
				tokenizer = null;
			}
			catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}
	    
	    private String next() {
	        while (tokenizer == null || !tokenizer.hasMoreTokens())
	            try {
	            	tokenizer = new StringTokenizer(br.readLine());
	            }
	            catch (IOException e) {
	                throw new RuntimeException(e);
	            }
	        return tokenizer.nextToken();
	    }
		public String nextLine() {
			try	{
				return br.readLine();
			}
			catch(Exception e) {
				throw(new RuntimeException());
			}
		}

	    int nextInt() {
	        return Integer.parseInt(next());
	    }
	    double nextDouble() {
	        return Double.parseDouble(next());
	    }	    
	    BigInteger nextBigInteger() {
	        return new BigInteger(next());
	    }
	    BigDecimal nextBigDecimal() {
	        return new BigDecimal(next());
	    }
	}
}